Algebra Math Calculator guide
Algebra Math Calculator: Solve Equations Step by Step
Use our algebra math calculator to solve linear, quadratic and simultaneous equations, with every step shown so you can follow the method for GCSE maths.
By the AllCalculator editorial teamUpdated 15 October 20263 min read
Algebra is about finding an unknown number from the clues an equation gives you. Once you know the method for each type of equation, the steps are the same every time. Our Algebra Math Calculator solves the three types you'll meet most often and shows each step, so you can check your working rather than just copy an answer.
Linear equations
A linear equation looks like ax + b = c. To solve it, do the same thing to both sides until x is on its own:
- Subtract b from both sides: ax = c − b
- Divide both sides by a: x = (c − b) ÷ a
For 3x + 4 = 19: 3x = 15, so x = 5. Check it: 3 × 5 + 4 = 19.
Quadratic equations
A quadratic looks like ax² + bx + c = 0. The quadratic formula always works:
x = (−b ± √(b² − 4ac)) ÷ 2a
The part under the square root, b² − 4ac, is called the discriminant:
- If it's positive, there are two solutions.
- If it's zero, there's one repeated solution.
- If it's negative, there are no real solutions.
For x² − 5x + 6 = 0, the discriminant is 25 − 24 = 1, so x = (5 ± 1) ÷ 2, giving x = 3 or x = 2.
Simultaneous equations
Two equations with two unknowns, x and y, can be solved together. For example:
- 2x + 3y = 13
- x − y = 1
From the second, x = y + 1. Substituting into the first: 2(y + 1) + 3y = 13, so 5y = 11, giving y = 2.2 and x = 3.2. The calculator uses an equivalent method, so you'll get the same answer.
If the two equations describe parallel lines, there's no solution. If they're the same line, there are infinitely many.
How to use the calculator (Algebra Math Calculator)
- Choose the type of equation.
- Enter the numbers in the boxes. Use a minus sign for negative numbers.
- Read the solution and the steps underneath.
Tips for checking your answers
- Substitute your answer back in. If both sides match, it's right.
- Watch your signs. Most mistakes come from a minus sign that's been dropped.
- Show your method in exams. You usually get marks for the working, even if the final answer is wrong.
For other everyday maths, try our Percentage Calculator or Calculator to Find Percentage.
Frequently asked questions
How do I solve for x?
Get x on its own by doing the same operation to both sides of the equation. Undo addition with subtraction and multiplication with division, in reverse order.
What does it mean if a quadratic has no real solutions?
The discriminant, b² − 4ac, is negative, so the graph of the quadratic doesn't cross the x-axis. The solutions are complex numbers, which the calculator shows using i.
Can I use this for homework?
Yes, but try the question yourself first and use the calculator to check. Following the steps shown helps you learn the method.
Practise a few of each type and the methods soon become second nature. Use the Algebra Math Calculator to check your answers as you go.
Sources and further reading
Links open official and independent websites in a new tab.
This guide is general information to help you understand your options. It isn't financial, tax, legal or building advice and doesn't take your personal circumstances into account. Figures were checked when the guide was last updated and can change, so confirm anything important with GOV.UK, HMRC, a regulated adviser or a qualified tradesperson.